Kinetic Energy
Kinetic energy
Kinetic energy is the energy an object possesses due to its motion.
It depends on two factors:
- Mass of the object ($m$)
- Speed of the object ($v$)
The formula for kinetic energy is:
$$E_k = \frac{1}{2}mv^2$$
TipKinetic energy is a scalar quantity, meaning it has magnitude but no direction.
A car of mass 1000 kg is moving at a speed of $20 \ \text{m s}^{-1}. What is its kinetic energy?
Solution
- Use the formula for kinetic energy:$$E_k = \frac{1}{2}mv^2$$
- Substitute the values:$$E_k = \frac{1}{2} \times 1000 \, \text{kg} \times (20 \, \text{m s}^{-1})^2$$
- Calculate:$$E_k = 200,000 \, \text{J}$$
- The car's kinetic energy is 200,000 J (joules).
Potential Energy
Potential energy
Potential energy is the energy stored in an object due to its position or configuration.
There are two main types of potential energy:
- Gravitational Potential Energy
- Elastic Potential Energy
Gravitational Potential Energy
Gravitational potential energy
Gravitational potential energy is the energy stored due to the position of an object in a gravitational field.
The formula for gravitational potential energy is:
$$E_p = mgh$$
where:
- $m$ is the mass of the object
- $g$ is the acceleration due to gravity (approximately $9.81 \ \text{m s}^{-2}$ on Earth)
- $h$ is the height above the reference point
A rock of mass 5 kg is lifted to a height of 10 m. What is its gravitational potential energy?
Solution
- Use the formula for gravitational potential energy:$$E_p = mgh$$
- Substitute the values:$$E_p = 5 \, \text{kg} \times 9.81 \, \text{m s}^{-2} \times 10 \, \text{m}$$
- Calculate:$$E_p = 490.5 \, \text{J}$$
- The rock's gravitational potential energy is 490.5 J.
- Note that $E_p = mgh$ is only valid for small height changes near a planet's surface.
- For larger distances, the formula $E_p = -\frac{GMm}{r}$ must be used.
Elastic Potential Energy
Elastic potential energy
Elastic potential energy is the energy stored in an elastic object, such as a spring, when it is compressed or stretched.
The formula for elastic potential energy is:
$$E_e = \frac{1}{2}kx^2$$
where:
